$A$ $B$ $C$ If: $ AC = 74$, $ AB = 5x + 6$, and $ BC = 5x + 8$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {5x + 6} + {5x + 8} = {74}$ Combine like terms: $ 10x + 14 = {74}$ Subtract $14$ from both sides: $ 10x = 60$ Divide both sides by $10$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 5({6}) + 8$ Simplify: $ {BC = 30 + 8}$ Simplify to find ${BC}$ : $ {BC = 38}$